1. Fitting covariance matrix models to simulations
- Author
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Alessandra Fumagalli, Matteo Biagetti, Alex Saro, Emiliano Sefusatti, Anže Slosar, Pierluigi Monaco, Alfonso Veropalumbo, Fumagalli, Alessandra, Biagetti, Matteo, Saro, Alexandro, Sefusatti, Emiliano, Slosar, Anze, Monaco, Pierluigi, and Veropalumbo, Alfonso
- Subjects
dark matter simulation ,dark matter simulations ,Cosmology and Nongalactic Astrophysics (astro-ph.CO) ,Bayesian reasoning ,FOS: Physical sciences ,Astronomy and Astrophysics ,cosmological parameters from LSS ,85A40 ,galaxy clustering ,Astrophysics - Cosmology and Nongalactic Astrophysics - Abstract
Data analysis in cosmology requires reliable covariance matrices. Covariance matrices derived from numerical simulations often require a very large number of realizations to be accurate. When a theoretical model for the covariance matrix exists, the parameters of the model can often be fit with many fewer simulations. We write a likelihood-based method for performing such a fit. We demonstrate how a model covariance matrix can be tested by examining the appropriate $\chi^2$ distributions from simulations. We show that if model covariance has amplitude freedom, the expectation value of second moment of $\chi^2$ distribution with a wrong covariance matrix will always be larger than one using the true covariance matrix. By combining these steps together, we provide a way of producing reliable covariances without ever requiring running a large number of simulations. We demonstrate our method on two examples. First, we measure the two-point correlation function of halos from a large set of $10000$ mock halo catalogs. We build a model covariance with $2$ free parameters, which we fit using our procedure. The resulting best-fit model covariance obtained from just $100$ simulation realizations proves to be as reliable as the numerical covariance matrix built from the full $10000$ set. We also test our method on a setup where the covariance matrix is large by measuring the halo bispectrum for thousands of triangles for the same set of mocks. We build a block diagonal model covariance with $2$ free parameters as an improvement over the diagonal Gaussian covariance. Our model covariance passes the $\chi^2$ test only partially in this case, signaling that the model is insufficient even using free parameters, but significantly improves over the Gaussian one., Comment: Accepted for publication in JCAP. 24 pages, 8 figures
- Published
- 2022